Question 18
Three girls $A,B,C$ and seven boys are lined up in a row. Let $n$ be the number of arrangements in which $B$ lies between $A$ and $C$, and exactly four boys separate $A$ and $B$. Determine $\left\lfloor n/5!\right\rfloor$.
Counting convention: all ten people are distinct. The brackets denote the floor, the greatest integer not exceeding the enclosed value.
Counting convention: all ten people are distinct. The brackets denote the floor, the greatest integer not exceeding the enclosed value.